To find the inverse of the function [tex]\( f(x) = \frac{1}{4}x - 12 \)[/tex], follow these steps:
1. Rewrite the function as [tex]\( y = \frac{1}{4}x - 12 \)[/tex]:
[tex]\[
y = \frac{1}{4}x - 12
\][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to find the inverse function:
[tex]\[
x = \frac{1}{4}y - 12
\][/tex]
3. Solve the equation for [tex]\( y \)[/tex]:
- First, add 12 to both sides:
[tex]\[
x + 12 = \frac{1}{4}y
\][/tex]
- Next, multiply both sides by 4 to isolate [tex]\( y \)[/tex]:
[tex]\[
4(x + 12) = y
\][/tex]
[tex]\[
y = 4x + 48
\][/tex]
4. Therefore, the inverse function [tex]\( h(x) \)[/tex] is:
[tex]\[
h(x) = 4x + 48
\][/tex]
Given the options:
- [tex]\( h(x) = 48x - 4 \)[/tex]
- [tex]\( h(x) = 48x + 4 \)[/tex]
- [tex]\( h(x) = 4x - 48 \)[/tex]
- [tex]\( h(x) = 4x + 48 \)[/tex]
The correct inverse function is:
[tex]\[
h(x) = 4x + 48
\][/tex]
So the correct option is:
[tex]\[
h(x)=4x+48
\][/tex]
